Apparatus and method for controlling ranging depth in optical frequency domain imaging

ABSTRACT

Exemplary embodiments of an apparatus are provided. For example, the exemplary apparatus can include at least one first arrangement providing at least one first electro-magnetic radiation to a sample, at least one second electro-magnetic radiation to a first reference and at least one third electro-magnetic radiation to a second reference. A frequency of radiation provided by the first arrangement generally varies over time. The exemplary apparatus may also include at least one second arrangement which is configured to detect a first interference between at least one fourth electro-magnetic radiation associated with the first electro-magnetic radiation and at least one fifth electro-magnetic radiation associated with the second radiation. The second arrangement is also configured to detect a second interference between at least one sixth electro-magnetic radiation associated with the first electro-magnetic radiation and at least one seventh electro-magnetic radiation associated with the third radiation.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application is based upon and claims the benefit of priority fromU.S. Patent Application Ser. No. 60/885,652, filed Jan. 19, 2007, theentire disclosure of which is incorporated herein by reference.

FIELD OF THE INVENTION

The present invention relates generally to apparatus and method forcontrolling (e.g., increasing) ranging depth in optical frequency domainimaging by using one or more depth and frequency encoding (“DFE”)technique.

BACKGROUND INFORMATION

Optical coherence tomography (“OCT”) techniques provide exemplarycross-sectional images of biological samples with resolution on thescale of several to tens of microns. Contrast in conventional OCTresults from differences in the optical scattering properties of varioustissues and permits imaging of tissue microstructure. It has beendemonstrated that Fourier-Domain OCT (“FD-OCT”) provides significantlyimproved sensitivity, enabling high-speed imaging. FD-OCT has beenimplemented in two configurations, spectral-domain OCT (“SD-OCT”) andoptical frequency domain imaging (“OFDI”). In exemplary SD-OCTarrangement as shown in FIG. 1( a), a spectrometer can be used to recordspectral fringes that result from the interference of a reference beamwith light reflected from a sample. In the exemplary OFDI arrangement asshown in FIG. 1( b), a narrowband wavelength-swept source and a singledetector are used to record the same interferogram.

The exemplary OFDI arrangements and methods, however, may become thepreferred imaging modalities for several applications since they may beless prone to motion artifacts associated with endoscopy and can providea larger depth range. However, the maximum ranging depth can typicallybe limited by the instantaneous line-width (coherence length) of thelaser source. For a number of OFDI sources, there may be a tradeoffbetween instantaneous line-width, tuning speed, output power, and tuningrange, which ultimately limits the useful ranging depth. Several methodshave been described to avoid the ambiguity between positive and negativedepths and increase ranging depth by measuring quadrature interferencesignals or using both sides of the coherence range. Continueddevelopment of wavelength-swept laser sources can provide furtherimprovements in imaging speed and resolution. These advantages areimportant in several exemplary OCT applications, including Barrett'sesophagus screening and coronary imaging. As such, imaging in manyapplications may require increasing ranging depth.

One of the objects of the present invention is to overcome theabove-described deficiencies.

SUMMARY OF EXEMPLARY EMBODIMENTS OF PRESENT INVENTION

According to certain exemplary embodiments of the present invention,method and apparatus for making high ranging depth measurements by usingdepth and frequency encoding (“DFE”) in an exemplary OFDI system can beprovided. For example, the exemplary embodiments of the method andapparatus can utilize a technique for increasing the ranging depth usingdepth and frequency encoding in OFDI. This exemplary technique can use,e.g., two (N) acousto-optic frequency shifters in two (N) differentreference arms to provide two (N) constant frequency shifts in thedetected signal. The path differences may divide the ranging depth intotwo (N) sections, where each section can be encoded by a differentfrequency.

Measurement of amplitude and phase can be used to measure profilereflectivity of the sample, blood flow and other motion in a turbid orscattering media, can also be used to monitor optical thickness ofmaterials over time or as a function of transverse location, and can beused to measure birefringence of the sample. An exemplary embodiment ofthe apparatus and method according to the present invention can be usedfor increasing ranging depth in the above measurement methods. In thisexemplary embodiment, the OFDI system can be modified to simultaneouslyacquire, e.g., two (N) images of the sample at two (N) differentsections where each image is encoded by a different frequency.

Thus, exemplary embodiments of an apparatus according to the presentinvention are provided. For example, the exemplary apparatus can includeat least one first arrangement providing at least one firstelectro-magnetic radiation to a sample, at least one secondelectro-magnetic radiation to a first reference and at least one thirdelectro-magnetic radiation to a second reference. A frequency ofradiation provided by the first arrangement generally varies over time.The exemplary apparatus may also include at least one second arrangementwhich is configured to detect a first interference between at least onefourth electro-magnetic radiation associated with the firstelectro-magnetic radiation and at least one fifth electro-magneticradiation associated with the second radiation. The second arrangementis also configured to detect a second interference between at least onesixth electro-magnetic radiation associated with the firstelectro-magnetic radiation and at least one seventh electro-magneticradiation associated with the third radiation.

According to another exemplary embodiment of the present invention, anoptical path length of the first reference may be substantiallydifferent from an optical path length of the second reference. Thedifference between the optical path length of the first reference andthe optical path length of the second reference can be more than 500 μm.Further, the first reference may have a further arrangement to shift afrequency of the second electro-magnetic radiation. In addition, thefirst reference may have an additional arrangement to shift a frequencyof the third electro-magnetic radiation.

According to yet another exemplary embodiment of the present invention,the magnitude of the shift of the frequency of the secondelectro-magnetic radiation can be different from a magnitude of theshift of the frequency of the third electro-magnetic radiation. Thefirst electro-magnetic radiation can have a spectrum whose meanfrequency may change substantially continuously over time at a tuningspeed that is greater than 100 Tera Hertz per millisecond.

These and other objects, features and advantages of the presentinvention will become apparent upon reading the following detaileddescription of embodiments of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

Further objects, features and advantages of the invention will becomeapparent from the following detailed description taken in conjunctionwith the accompanying figures showing illustrative embodiments of theinvention, in which:

FIG. 1A is a schematic diagram of a conventional spectral-domain OCTsystem;

FIG. 1B is a schematic diagram of a conventional OFDI system;

FIG. 1C is a schematic diagram of a conventional OFDI system forincreasing ranging depth by measuring quadrature interference signals;

FIG. 1D is a schematic diagram of a conventional OFDI system forincreasing ranging depth using both sides of the coherence range;

FIG. 2A is a schematic diagram of an exemplary operation of an exemplaryembodiment of a system according to the present invention implementingan exemplary embodiment of a depth and frequency encoding technique;

FIG. 2B is a plot of an exemplary crosstalk caused by two depths mappedto the same frequency;

FIG. 3 is a block diagram of another exemplary embodiment of the systemaccording to the present invention which utilized an exemplary depth andfrequency encoding technique;

FIGS. 4( a)-4(d) are plots of variations of (a, b) SIR1 and (c, d) SIR2due to A-line rate and frequency spacing;

FIG. 5 is a plot of a minimum SIR for different tuning speeds;

FIG. 6 is a plot of an exemplary signal power variation by moving acalibrated partial reflector (sample) throughout the total rangingdepth;

FIG. 7( a) is a side view of an exemplary OFDI image of the human aortatissue ex vivo obtained with frequency shifts 25 and 50 MHz, with theexemplary image consisting of 1492 vertical×500 transverse pixels,whereas the depth and frequency encoding technique increased the rangingdepth to 10 mm;

FIG. 7( a) is an end view of the exemplary OFDI image of the human aortatissue ex vivo of FIG. 7( b);

FIG. 8 is an exemplary image of the tissue before the application of theexemplary embodiment of the technique according to the presentinvention, and an exemplary image thereof after the application of theexemplary technique; and

FIG. 9 is a flow diagram of a method according to an exemplaryembodiment of the present invention.

Throughout the figures, the same reference numerals and characters,unless otherwise stated, are used to denote like features, elements,components or portions of the illustrated embodiments. Moreover, whilethe subject invention will now be described in detail with reference tothe figures, it is done so in connection with the illustrativeembodiments. It is intended that changes and modifications can be madeto the described embodiments without departing from the true scope andspirit of the subject invention.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

Convention OFDI systems can create images based on the magnitude andphase of the reflectivity as a function of depth. In this OFDI system,the maximum ranging depth is typically limited by the instantaneousline-width (coherence length) of the laser source because one side ofcoherence range is used by placing the zero depth at the surface of thesample to avoid the ambiguity between positive and negative depths.Other methods have been discussed to avoid the ambiguity betweenpositive and negative depths and increase ranging depth including: I)measuring quadrature interference signals shown in FIG. 1( c) or II)using both sides of the coherence range shown in FIG. 1( d). The firstapproach can unfold otherwise overlapping images associated withpositive and negative depths, but tended to leave residual artifacts dueto the difficulty of producing stable quadrature signals. The secondapproach can provide a 2-fold increase of the effective ranging depth.

According to the exemplary embodiment of the present invention, methodand apparatus can be provided for an N-fold increase of the effectiveranging depth. N different frequency shifts are applied into N differentreference arms to provide N constant frequency shifts in the detectedsignal. The path differences divide the ranging depth into N sections,where each section is encoded by a different frequency. FIG. 2 (a)depicts a schematic of the depth and frequency encoding setup. Byassuming a Gaussian coherence function, the fringe visibility has a peakvalue at the zero path difference point and decreases as the pathdifference increases. The coherence length l_(c) indicates the deptharound the zero path difference point where the visibility drops to 0.5and thereby the SNR drops by 6 dB. In the proposed technique, the numberof zero path difference points (depths) inside the sample is increasedby a factor of N (points A₁ and A_(N)) using N reference arms biasedrelative to each other (Δz). As shown in the example of FIG. 2 (a), withone frequency shifter only a single coherence region can be used.However, N coherence regions can be utilized by dividing the sample intoN sections and frequency multiplexing each section.

While this exemplary technique can provides a N-fold increase of theeffective ranging depth of a conventional OFDI system, two factors candegrade the image quality including: I) crosstalk (interference) betweenadjacent encoded images at different frequencies and II) crosstalkbetween a specific depth that corresponds to a frequency

$\left( {\left( {f_{i} - f_{j}} \right) + \frac{2\;\Delta\; z\;\Delta\;\lambda}{\lambda_{0}^{2}T}} \right)$and the third term in equation (5), where Δλ,λ₀, and T are the sourcetuning range, center wavelength, and tuning period.

Explanation of OFDI in Frequency Domain

Exemplary Fourier-Domain OCT systems and methods generally use theinterference between two arms of an interferometer to measuredepth-dependent reflections in a turbid, semi-turbid, or transparentmedium. An input light source is split into a reference arm and a samplearm. The light in the sample arm is directed to the sample to be imaged,and reflections from the sample are directed to a first port of anoutput coupler. The reference arm light is directed to the second portof the same output coupler. Spectral interference between the beams ismeasured by recording the interferometer output power as a function ofwave-number (or time). The balanced detected current can be expressedas:i _(s)(t)=2η√{square root over (P _(r)(t)P _(s)(t))}{square root over (P_(r)(t)P _(s)(t))}∫√{square root over (R(z))}G(|z _(r) −z|){cos(2k(t)(z_(r) −z)+φ_(z))dz  (1)where η, Pr(t), Ps(t), R(z), G(|z_(r) −z|), k(t), φ_(z) and Δz=z_(r)−zare the quantum efficiency of the detector, the reference arm opticalpower, the sample arm optical power, the sample reflectivity profile,coherence function corresponding to the fringe visibility, wavenumber,the phase of the reflection at position z and the path differencebetween reference arms and an scatterer at position z. By assuming theoutput wavenumber is tuned linearly in time i.e. k(t)=k₀−k₁t, wherek=2π/λ is the wavenumber, λ is the optical wavelength, t is the timespanning from −T/2 to T/2, and T is the tuning period or equivalentlyA-line period. Further we assume a Gaussian tuning envelope given by

$\begin{matrix}{{P_{out}(t)} = {P_{out}{\exp\left( {- \frac{\left( {4\;\ln\; 2} \right)t^{2}}{\left( {\sigma\; T} \right)^{2}}} \right)}}} & (2)\end{matrix}$where P_(out)(t) denotes the output power of the source and σT the fullwidth at half maximum (FWHM) of the tuning envelope. Eq. (2) alsodescribes the Gaussian spectral envelope of the source, where σk₁Tcorresponds to the FWHM tuning range in wavenumber. A Fourier transformof Eq. (1) with respect to t yields a complex-valued depth profile(A-line).

Assuming:

${\sqrt{{P_{r}(t)}{P_{s}(t)}} = {P_{out}{\exp\left( {- \frac{\left( {4\;\ln\; 2} \right)t^{2}}{\left( {\sigma\; T} \right)^{2}}} \right)}}},{k_{1} = \frac{2\;\pi\;\Delta\;\lambda}{\lambda_{0}^{2}T}}$and σ<1, we can approximate the range of the integral to [−∞, +∞], whichresults in

$\begin{matrix}\begin{matrix}{{I(f)} = {F\left\{ {i_{s}(t)} \right\}}} \\{= {\int_{- \frac{T}{2}}^{\frac{T}{2}}{{i_{s}(t)}{\exp\left( {{\mathbb{i}}\; 2\;\pi\; f\; t} \right)}\ {\mathbb{d}t}}}} \\{= {2\;\eta\; P_{out}{\int{\sqrt{R(z)}{G\left( {{z_{r} - z}} \right)}}}}} \\{\int_{- \frac{T}{2}}^{\frac{T}{2}}{\cos\left\lbrack {{2\left( {k_{0} - {k_{1}t}} \right)\left( {z_{r} - z} \right)} + \phi_{z}} \right\rbrack}} \\{{\exp\left( {{{\mathbb{i}}\; 2\;\pi\; f\; t} - \frac{\left( {4\;\ln\; 2} \right)t^{2}}{\left( {\sigma\; T} \right)^{2}}} \right)}{\mathbb{d}t}{\mathbb{d}z}} \\{= {\frac{\eta\; P_{out}\sigma\; T}{2}\sqrt{\frac{\pi}{\ln(2)}}{\int{\sqrt{R(z)}{G\left( {{z_{r} - z}} \right)}}}}} \\{\left\lbrack {\exp\left\{ {{- {\frac{\left( {\sigma\; T} \right)^{2}}{16\;{\ln(2)}}\left\lbrack {{2\;\pi\; f} - {\frac{4\;\pi\;\Delta\;\lambda}{\lambda_{0}^{2}T}\left( {z_{r} - z} \right)}} \right\rbrack}^{2}} +} \right.} \right.} \\{\left. {{\mathbb{i}}\left( {{2\;{k_{0}\left( {z_{r} - z} \right)}} + \phi_{z}} \right)} \right\} +} \\{\exp\left\{ {{- {\frac{\left( {\sigma\; T} \right)^{2}}{16\;{\ln(2)}}\left\lbrack {{2\;\pi\; f} + {\frac{4\;\pi\;\Delta\;\lambda}{\lambda_{0}^{2}T}\left( {z_{r} - z} \right)}} \right\rbrack}^{2}} -} \right.} \\{\left. \left. {{\mathbb{i}}\left( {{2\;{k_{0}\left( {z_{r} - z} \right)}} + \phi_{z}} \right)} \right\} \right\rbrack{\mathbb{d}z}}\end{matrix} & (3)\end{matrix}$As show in the above equation (3), the backscattering coefficient of thescatterer at position z is given by the magnitude of the signal atfrequency

${\pm \frac{2\;\Delta\;\lambda}{\lambda_{0}^{2}T}}{\left( {z_{r} - z} \right).}$There is interference between frequency components correspond to±(z_(r)−z) depths limiting using both side of coherence function(G(|z|)).

Depth and Frequency Encoding in OFDI

Exemplary FD-OCT techniques of SD-OCT and OFDI systems and methods canmeasure the discrete spectral interference i(k) but differ in theimplementation of this measurement. OFDI uses a wavelength-swept sourceand a single-element photoreceiver (or set of single-elementphotoreceivers) to record i(k) as a function of time. FIG. 3 shows anexemplary embodiment of a high-speed OFDI imaging system. This exemplarysystem can include, e.g., three modules: a wavelength-swept source 85,an interferometer 90, and acquisition electronics 95. Thewavelength-swept source (hereafter referred to as swept source) isconstructed as a ring-cavity laser with a semiconductor opticalamplifier (SOA) 125 as the gain element and a polygon mirror filter 101comprising a polygon mirror 100, telescope 105, diffraction grating 110,and fiber collimator 113. A polarization controller 120 can be insertedto optimize the laser polarization and output coupler 130 provides thelaser output. The output coupler can nominally split light equallybetween the output port 132 and laser port 131. An optical circulator115 directs light from the laser port 131 to the polygon mirror filter101, and may direct light returning from the polygon mirror filter 101to the polarization controller 120. As the polygon mirror rotates, thewavelength reflected from the polygon mirror filter 101 sweeps inwavelength, causing the laser output to sweep in wavelength in a similarmanner.

The laser output at 132 can therefore be wavelength swept in time. Thisoutput is input to the interferometer coupler 135 which splits the lightinto a reference arm port 135 a and sample arm port 135 b. Coupler 165splits the reference arm light. Light from the output 165 a is directedto a second circulator 145 which passes light to a fiber Bragg grating(FBG) 150. The FBG has a narrowband reflection at a discrete wavelengthwithin the wavelength-sweep range of the source. As the source tunespast this reflection wavelength, a reflected optical pulse is generated.This pulse is directed by the circulator 145 to the photoreceiver 155after which it is converted into a TTL pulse by 160. This TTL pulse isused as a trigger signal for the data acquisition electronics 200. Lightfrom output port 165 b is directed to a third circulator which directslight to a variable optical delay 210. This variable optical delay isused to path-match the interferometer. Return light is directed by thecirculator 170 to the first port 220 a of the input coupler 220. Thelight at the Nth port 220N of the output coupler 220 is directed to thepolarization controller 225N and frequency shifter 230N at frequencyfs_(N) and the polarizer 235N. The frequency shifter 230N in thereference arm is driven through a signal carried on line 203 which isderived from the DAQ sample clock output 204.

This output clock is down-shifted in frequency using a “Divide by N”digital logic circuit 201 and the resulting signal passes through anamplifier and filter stage 202 to produce a single tone on line 203.Because the drive signal for the frequency shifter is driven by the DAQsample clock output, the phase of the frequency shift is synchronouswith the sample clock and thus does not induced additional phase noise.Then, light is directed to the polarization controller 240N and the Nthport 245N of the input coupler 245. All N frequency shifted lights arecombined at the first port 245 of the output coupler 245 and directed tothe first port 250 a of the input coupler 250. By assuming the pathdifference between the i-th port 220 i of the input coupler 220 and thei-th port 245 i of the input coupler 245 is Li, we set the differencebetween Li and Lj to 4*(N−M)*Lc, where Lc is the coherence length of thesource. The sample arm light at port 135 b is directed to a fourthcirculator 205 which directs the light on fiber 206 to the sample to beimaged. Imaging optics 215 focuses the light on the sample and providefor beam translation.

Light reflected from the sample is collected by the same fiber 206 andreturned to circulator 205 which directs the light to a frequencyshifter and the second port 250 b of the input coupler 250. Thisfrequency shifter that is not driven is used to compensate for thedispersion of the driven frequency shifters. The combined sample armlight and reference arms light at the first port 250 c and 250 d of theoutput coupler 250 are directed to polarization controllers 260 and 270and polarization beam splitter 280 and 290, respectively. By adjustingthe polarization controllers 240 i, the polarization states of shiftedlight become parallel to each other at the input ports of polarizationbeam splitters 280 and 290. By adjusting the polarization controllers260 and 270, The power of the output coupler 250 correspond to the Nthreference arm power equally splits between the first and second ports280 a, 280 b, 290 a, and 290 b of the output polarization beam splitters280 and 290. Reference arms and sample arm light interferes at the firstand second ports 280 a, 280 b, 290 a, and 290 b of the outputpolarization beam splitters 280 and 290. The interference signal at thefirst ports 280 a of the output polarization beam splitters 280 and thefirst ports 290 a of the output polarization beam splitters 290 aredetected by the photoreceiver 295 a and 295 b, respectively.

The interference signal at the second ports 280 b of the outputpolarization beam splitters 280 and the second ports 290 b of the outputpolarization beam splitters 290 may be detected by the photoreceiver 300a and 300 b, respectively. The signals from the photoreceiver 295 a and295 b are subtracted and directed toward an analog-to-digital (A2D)input port of the data acquisition (DAQ) board 200. The signals from thephotoreceiver 300 a and 300 b are subtracted and directed toward ananalog-to-digital (A2D) input port of the data acquisition (DAQ) board.The DAQ board 200 acquires n (n is predetermined) samples at a clockrate f_(c1). The clock signal is internally generated in the DAQ board200. The trigger signal from the TTL pulse generator 160 originates fromthe optical pulse produced by the FBG 150. sections around correspondingzero depths (z_(r1), z_(r2)). When the A-line rate increases, SIRdecreases. For example SIR1 increases around 30 dB at zero depth whenthe tuning speed decreases from 75 KHz to 50 KHz with frequency spacing50 MHz. In addition, SIR at each depth grows when the frequency spacingincreases for a determined A-line rate.

The appropriate frequency spacing for a preferred SIR can depend on notonly the A-line rate but also coherence length. As shown in FIG. 2( b),the SIR increases by increasing coherence length. In theoretical,simulation, and experimental results, we assume the source instantaneouscoherence length and Δz are 2.5 mm and 5 mm respectively. FIG. 5 showsthe minimum SIR for different tuning speeds and frequency spacings (25MHz and 50 MHz). The simulation results in FIG. 6 shows signal powerversus depth using a calibrated partial reflector at various depthlocations in the sample arm. The lens and sample can be moved so thatthe sample reflectivity profile was uniform from −5 mm to 5 mm. Thesampled data acquired at each depth may be processed with mapping anddechirping procedures. The minimum SIR through the depth may be greaterthan 60 dB using an OFDI system with 25 KHz A-line rate, frequencyspacing 50 MHz, coherence length 2.5 mm, and tuning range 100 nm.

Exemplary Processing Procedure

Nonlinearity in the tuning frequency of the source results in a chirpingof the signal at a constant depth and causes a degradation of axialresolution. It is possible to a modify an exemplary interpolation methodbased on frequency shifting and zero padding to achieve nearly transformlimited axial resolution over the entire ranging depth. An exemplaryembodiment of a procedure to perform such exemplary function is shown inFIG. 9.

With frequency shifts f₁, . . . , f_(i) . . . , f_(N) in the referencearms 1100 i iε{1, . . . N} and an interferometer path-length differences(or depths) of z_(r1)-z, z_(r2)-z, z_(rN)-z, Signals at the output ofthe 295 and 300 photo-receivers can be expressed as:

$\begin{matrix}{{\left. {{i_{s}(t)} = {{2\;\eta\sqrt{{P_{r}(t)}{P_{s}(t)}}{\int{\sqrt{R(z)}\begin{Bmatrix}{\sum\limits_{i = 1}^{N}{G\left( {{z_{ri} - z}} \right)}} \\{\cos\begin{pmatrix}{{2\; k(t)\left( {z_{ri} - z} \right)} +} \\{{2\;\pi\; f_{i}t} + \phi_{z}}\end{pmatrix}}\end{Bmatrix}{\mathbb{d}z}}}} + {2\;\eta\;{P_{r}(t)}{\sum\limits_{j = 1}^{N}{\sum\limits_{i = 1}^{N}{\cos\left( {2\;{k(t)}\left( {z_{ri} - z_{rj}} \right)} \right)}}}} + {2\;{\pi\left( {f_{i} - f_{j}} \right)}t}}} \right)\mspace{79mu}{{{for}{\mspace{14mu}}i} \neq j}}\mspace{14mu}} & (4) \\\left. {{I(f)} = {{\quad\quad}{\quad{\quad\quad}\quad}\frac{\eta\; P_{out}\sigma\; T}{2}\sqrt{\frac{\pi}{\ln(2)}}{\int{\sqrt{R(z)}\left\{ {{\sum\limits_{i = 1}^{N}{{G\left( {{z_{ri} - z}} \right)}\left. \quad\left\lbrack \begin{matrix}{{\exp\begin{Bmatrix}{{- {\frac{\left( {\sigma\; T} \right)^{2}}{16\;{\ln(2)}}\left\lbrack {{2\;\pi\; f} - {\frac{4\;\pi\;\Delta\;\lambda}{\lambda_{0}^{2}T}\left( {z_{r} - z} \right)} + {2\;\pi\; f_{i}}} \right\rbrack}^{2}} +} \\{{\mathbb{i}}\left( {{2\;{k_{0}\left( {z_{ri} - z} \right)}_{i}} + \phi_{z}} \right)}\end{Bmatrix}} +} \\{\exp\begin{Bmatrix}{{- {\frac{\left( {\sigma\; T} \right)^{2}}{16\;{\ln(2)}}\left\lbrack {{2\;\pi\; f} + {\frac{4\;\pi\;\Delta\;\lambda}{\lambda_{0}^{2}T}\left( {z_{ri} - z} \right)} - {2\;\pi\; f_{i}}} \right\rbrack}^{2}} -} \\{{\mathbb{i}}\left( {{2\;{k_{0}\left( {z_{ri} - z} \right)}} + \phi_{z}} \right)}\end{Bmatrix}}\end{matrix} \right\rbrack \right\}{\mathbb{d} z}}} + {\frac{\eta\; P_{out}\sigma\; T}{2}\sqrt{\frac{\pi}{\ln(2)}}{\sum\limits_{j = 1}^{N}{\sum\limits_{i = 1}^{N}{\exp\begin{Bmatrix}{{- {\frac{\left( {\sigma\; T} \right)^{2}}{16\;{\ln(2)}}\begin{bmatrix}{{2\;\pi\; f} - {\frac{4\;\pi\;\Delta\;\lambda}{\lambda_{0}^{2}T}\left( {z_{ri} - z_{rj}} \right)} +} \\{2\;\pi\;\left( {f_{i} - f_{j}} \right)}\end{bmatrix}}^{2}} +} \\{{\mathbb{i}}\left( {{2\;{k_{0}\left( {z_{ri} - z_{rj}} \right)}_{i}} + \phi_{z}} \right)}\end{Bmatrix}}}}} + {\exp\begin{Bmatrix}{{- {\frac{\left( {\sigma\; T} \right)^{2}}{16\;{\ln(2)}}\begin{bmatrix}{{2\;\pi\; f} + {\frac{4\;\pi\;\Delta\;\lambda}{\lambda_{0}^{2}T}\left( {z_{ri} - z_{rj}} \right)} -} \\{2\;{\pi\left( \;{f_{i} - f_{j}} \right)}}\end{bmatrix}}^{2}} -} \\{{\mathbb{i}}\left( {{2\;{k_{0}\left( {z_{ri} - z_{rj}} \right)}} + \phi_{z}} \right)}\end{Bmatrix}}} \right\rbrack}}}} \right\} & (5)\end{matrix}$Equation (5) shows that the sample reflectivity profile is encoded at Ndifferent frequency shifts while zero depths of N interferometerscorrespond to f₁, . . . , f_(N). The third term of equation (5) is thebeat terms between N reference arm signals.

Signal to Interference Ratio (SIR)

Crosstalk between two adjacent encoded images causes degradation ofsensitivity and ranging depth. However, appropriate spacing betweenfrequency shifts can avoid crosstalk. As shown in FIG. 2( b), two depthsmapped into the same frequency range can cause crosstalk. For twofrequency shifts, the theoretical results in FIG. 3 shows that theproper frequency spacing for required SIR depends on the A-line rate(assuming crosstalk is dominant term in the presence of noise). FIGS. 4(a), (b), (c), and (d) show the variation of SIR due to depth fordifferent frequency spacings and A-line rates. SIR1 and SIR2 are signalto interference ratios of two

In particular, as illustrated in FIG. 9, P samples of the signal areobtained with uniform time interval during each wavelength sweep of thesource (procedure 910). DFT of P data points is then determined in theelectrical frequency domain (procedure 920). Further, 2P frequency bandsare separated below and above frequency shifts f_(i)ε{f₁, . . . , f_(N)}corresponding negative and positive depths, respectively (procedure930). Each frequency band can be shifted such that the zero depth isaligned the zero electrical frequency (procedure 940). In addition,zero-padding can be applied to each frequency band and calculate inverseresulting in an array of increased number of samples in the time domainwith smaller time interval for each frequency band (procedure 950). Thenumber of zeroes can be determined based on required ranging depth. Eacharray in the time domain can be interpolated into a uniform v spaceusing a mapping function calibrated to the nonlinearity of the sourcewith linear interpolation (procedure 960). Then, DFT of eachinterpolated array can be determined (procedure 970). Further, the 2Parrays (e.g., images) can be combined by shifting the array index(procedure 980).

Exemplary Applications of DFE OFDI

In a further exemplary embodiment, the DFE-OFDI system can be used toimage intravascular. A device capable of imaging increasing rangingdepth is shown in FIG. 7. The optical probe 310 is placed inside theartery 320 and the imaging beam 330 is emitted from the side of theprobe. By moving probe into the artery, the imaging beam 330 hits artery320 at two different points A and B. DFE-OFDI is able to image artery atA and B while the images are encoded with different frequency. The endview illustrates how DFE-OFDI is able to increase ranging depth.

It can be appreciated by those skilled in the art that one of theembodiments can be used in combination with other embodiments toconstruct DFE-OFDI systems with increasing ranging depth.

EXAMPLE

The exemplary embodiment of the method according to the presentinvention was verified in the laboratory by the following experiment.

FIG. 1( a) depicts the experimental setup of the conventional OFDIsystem employing two acousto-optic frequency shifters (25 MHz and 50MHz). A swept laser was constructed to provide a tuning range of 117from 1240 nm to 1357 nm. The laser was operated at rates of 12.5 KHz, 25KHz and 50 KHz so that 15872, 7936, 3968 samples could be acquired(sampling rate ˜4 times of the maximum frequency shift). The probe,comprising a galvanometer mirror and an imaging lens, produced a 40 μm1/e² diameter focal spot on the sample with a confocal parameter of 2mm. An image of a human aorta was acquired ex vivo at an A-line rate of12.5 KHz with the depth and frequency-encoded OFDI system. This imagewas reconstructed using the mapping algorithm described above. Thesurface of the tissue was placed at an angle with respect to the probebeam axis, and the reference mirrors were positioned such that the pathdifference between them was 5 mm. The sample lens was configured tofocus the light 5 mm inside the tissue at the center of the image. FIG.7 (a) depicts an image of the aorta when we used a single frequencyshifter at 25 MHz for resolving positive and negative depth ambiguity.FIG. 7 (b) depicts the same image after depth and frequency encoding.The left and right sides of image were encoded at 25 MHz and 50 MHzfrequencies, respectively. The ranging depth was increased by a factorof two compared to the single frequency shifter case.

The foregoing merely illustrates the principles of the invention.Various modifications and alterations to the described embodiments willbe apparent to those skilled in the art in view of the teachings herein.Indeed, the arrangements, systems and methods according to the exemplaryembodiments of the present invention can be used with any OCT system,OFDI system, spectral domain OCT (SD-OCT) system or other imagingsystems, and for example with those described in International PatentApplication PCT/US2004/029148, filed Sep. 8, 2004, U.S. patentapplication Ser. Nos. 11/266,779, filed Nov. 2, 2005, and 10/501,276,filed Jul. 9, 2004, the disclosures of which are incorporated byreference herein in their entireties. It will thus be appreciated thatthose skilled in the art will be able to devise numerous systems,arrangements and methods which, although not explicitly shown ordescribed herein, embody the principles of the invention and are thuswithin the spirit and scope of the present invention. In addition, tothe extent that the prior art knowledge has not been explicitlyincorporated by reference herein above, it is explicitly beingincorporated herein in its entirety. All publications referenced hereinabove are incorporated herein by reference in their entireties.

1. An apparatus comprising: a first arrangement providing a firstelectro-magnetic radiation to a sample, a second electro-magneticradiation to a first reference path and a third electro-magneticradiation to a second reference path, wherein a frequency of radiationprovided by the first arrangement varies over time; and a secondarrangement configured to simultaneously detect: (i) all depth pointsfor a first interference which is between a fourth electro-magneticradiation associated with the first electro-magnetic radiation and afifth electro-magnetic radiation associated with the second radiation,and (ii) all depth points for a second interference which is between thefourth electro-magnetic radiation and a sixth electro-magnetic radiationassociated with the third radiation.
 2. The apparatus according to claim1, wherein an optical path length of the first reference path issubstantially different from an optical path length of the secondreference path.
 3. The apparatus according to claim 2, wherein thedifference between the optical path length of the first reference andthe optical path length of the second reference path is more than 500μm.
 4. The apparatus according to claim 1, wherein the first referencepath has a further arrangement to shift a frequency of the secondelectro-magnetic radiation.
 5. The apparatus according to claim 4,wherein the second reference path has an additional arrangement to shifta frequency of the third electro-magnetic radiation.
 6. The apparatusaccording to claim 4, wherein a magnitude of the shift of the frequencyof the second electro-magnetic radiation is different from a magnitudeof the shift of the frequency of the third electro-magnetic radiation.7. The apparatus according to claim 1, wherein the firstelectro-magnetic radiation has a spectrum whose mean frequency changessubstantially continuously over time at a tuning speed that is greaterthan 100 Tera Hertz per millisecond.
 8. The apparatus according to claim1, wherein the fourth radiation is provided from a particular locationof the sample.
 9. The apparatus according to claim 1, further comprisinga third arrangement which is configured to generate a depth profile forat least one portion of the sample based on the first and secondinterferences.